Aircraft: SMALL AIRCRAFT
Phase of flight: Initial Approach
Anomaly: Aircraft Equipment Problem Less Severe; Deviation - Altitude Crossing Restriction Not Met; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy

It has been hard to fly during the pandemic; and the aircraft had been in for annual inspection; so I had not flown for two months. I went out for practice. I chose the back-course approach at ZZZ; as it can be challenging. Also; during recurrent training in Month; we had noticed some odd autopilot behavior when flying this approach. My aircraft has Garmin avionics but these are mated to an older analogue autopilot.By the time I was told to switch to ZZZ1 Approach; I was still at 12;000 feet and quite close to ZZZZZ intersection on the approach. When I gave my request for the approach; the controller gave me vectors to circle back to rejoin the course while descending to 4000 feet. She then cleared me for the approach. I believed she said 'Maintain 4000 until established...'; but in our later discussion she said her instruction was 'Maintain 4000 to ZZZZZ.' I believe I read back the former. In any case; when back on extended approach course; but a short distance before ZZZZZ; I began to descend further. The chart showed 3000 feet for the segment between ZZZZZ and ZZZZZ1; which is the FAF and 5.8NM from ZZZZZ. My GPS displayed an altitude of 3100 at ZZZZZ; which I believe is its indication of a safe altitude. So; I had set altitude capture for 3100 feet and was descending. The controller alerted me that she had expected 4000 feet to ZZZZZ. While we were discussing this; the autopilot failed to capture and the descent continued to 2900 feet. The controller told me to switch to tower.On my first attempt to call tower at ZZZ; I had not hit the switch correctly and was still with ZZZ1 approach. At the same time; I noticed the autopilot taking me off course for the approach and interrupted it while calling the tower. We were in the descent within the FAF by this time. The tower controller told me I was low for the course and left of course; and he asked if I was flying the approach visually instead of using the Back Course. Due to the autopilot issue; I was by that time flying visually. It was a clear VFR day; and at no time was I in close proximity to terrain or other aircraft. The problem arose for several reasons. The pilot (me) was rusty and needed practice. It was a mistake to do the more challenging BC approach as the first one. (After this event; I did the missed approach as planned at ZZZ and did two fine approaches at ZZZ1 and ZZZ2.) Also; I believe there anomalies with my avionics set-up and back-course approaches; and I should not have been trying to troubleshoot that as a single pilot; especially being a bit out of practice. Another contributor was my misunderstanding of the controller's instruction; along with using the 3000 foot altitude indicated on the chart for that segment ZZZZZ to ZZZZZ1) and the 3100 foot altitude indicated as the target for ZZZZZ on my GPS for the altitude I was trying to attain. All of these issues increased workload; which is better handled by an in-practice pilot (which is why I had gone out to practice). A final recommendation from this experience is that I will avoid flying BC approaches with my autopilot until I can do a flight with a competent pilot and avionics technician aboard. The BC approaches are quite rare; and almost all have GPS overlays nowadays. So; they are not really a high priority; I actually chosen this one to be challenging and give me practice monitoring the autopilot and taking over if it acted strangely. But given the altitude misunderstanding; resulting discussion; and then the strange autopilot behavior; it was a bit choppy. I flew the airplane in a safe manner throughout (there was no terrain issue along my path); but my adherence to published instructed and published altitudes on the approach was poor. Private Pilot reported the cause of the deviation was not flying for 2 months during the pandemic and was rusty and needed practice.